Here’s a more concrete example of what is happening. If we look at the web-site of one reputable supplier, Spirit Solar, we see that they offer several types of panel. The stand-outs are Sanyo’s “Hybrid Mono” products, with the HIT-N240SE10 achieving 19% efficiency. These are still just silicon based (I understand that best results will eventually be obtained with layered panels, each layer using a different technology to capture light of particular wavelengths), but optimised for efficiency. The Sanyos are just a tad more expensive than the bog-standard panels at 14-15% efficiency. But here’s what Spirit Solar say:

“The Sanyo are the most expensive per Watt of power generated. Their one big advantage is that by using a different ‘hybrid’ technology they give approximately 25% more power per square metre than any other panel. …the Sanyo gives 190 Watts per square metre, compared to between 134 [actually none are this low - the figure is presumably out of date and the text should read "141"] and 149 Watts per square metre for the other panels. The downside is that they currently cost around 50p more per Watt – so for a 2 kWp system you will pay around £1000 more if you choose Sanyo. So if you are wondering whether to buy Sanyo or not, ask yourself what are you trying to maximise – the total power you can squeeze out of your roof or your financial return? If your objective is simply to maximise the power output from your available roof space without regard to budget, then you should choose the Sanyo hybrids. Don’t choose the hybrids if you want to maximise your financial return.” [my stress]

You have to email for a quote, and PV prices are currently all over the place, but that extra £1000 is on a system costing at least £5000, probably somewhat more. That is, for 20% more, tops, you get 25% more power for a given area. No-brainer.

But, as discussed yesterday, the FIT scheme does not provide an incentive to maximise output per unit area.

In fact, the FIT scheme seems to have been devised with no thought as to the behaviour it will encourage. The sole goal seems to have been to “bung up a few solar PV panels”.

Another page on Spirit Solar’s rather informative site illustrates another problem. Scroll through some of the pictures of the company’s installations. There are a number of examples of roofs where far more area could have been covered with panels.

Why wouldn’t customers want to cover their whole roof? Because there’s no incentive to do so, of course. Many installations will be of 4kW capacity (4kWp, where p stands for “peak”) or slightly under. Why? Because larger schemes receive a lower tariff. In fact, as I understand it, and using the tariffs to be put in place from now on, there’s no point at all in putting up a scheme of 4-4.8kWp. That’s right – you get less for a 4.8kWp system than for one of 4kWp. (The generating tariff for a scheme up to 4kWp is 21p/kWh, whereas for 4-10kWp it’s only 16.8p/kWh, so schemes of 4-4.88kWp will earn less revenue than those of 4kWp or just less!).

Of course, this problem could be simply fixed by qualifying the first 4kWp for the higher tariff and only additional capacity for the lower rate. This would at least mean that solar PV generators have an incentive to cover the whole available roof area.

Another solution would be simply to have more bands. The worst thing about the whole scheme is that you need a large unshaded roof area to reach the optimal 4kWp (about 25m^2 for standard panels, 20m^2 for the Sanyos), so there should be bands for smaller roofs (say 1kWp and 2kWp, but this should be done on installation area as discussed yesterday) and to ensure larger roofs were fully utilized (say 6kWp, 8kWp as well as 10kWp, and more subdivisions up to 50kWp).

There is another problem, though, which is that the export tariff is only 3p/kWh. That is, if you use the electricity, you displace electricity (or gas) you would otherwise have had to buy for around 10p/kWh (or 5p/kWh for gas). Since most households would be hard pushed to make use of more than 4kW for any length of time (though I don’t see why solar PV generators don’t invest in a 20kW battery to store energy for the hours of darkness), this means the drop-off in revenue above 4kWp is even worse.

Surely the policy is eventually to generate electricity for sale to the grid. If this is the case, then shouldn’t the export tariff be somewhat higher? I gather the 3p/kWh is based on the wholesale price for electricity. But solar PV electricity is more useful than bog-standard electricity. It’s renewable for a start, so should qualify for ROCs (renewable obligation certificates) which otherwise cost money. And it’s at a peak time (except perhaps at weekends). One problem is that you don’t want the export tariff to exceed the retail gas price, because then solar PV generators have an incentive to use gas rather than electricity (since they can sell the electricity to pay for the gas and still be quids in), but there’s still scope for an increase to, say, 4.5p/kWh. This would make it a little more worthwhile for people to cover their whole roof with panels.

It may be worth DECC thinking through the FIT scheme a little more thoroughly, since these panels are going to last for decades – they’re typically guaranteed to provide at least 80% of their original output in 25 years. Once they’re up, it’s not going to be worth taking panels down – especially those qualifying for FITs – to replace them with more efficient technology.

Why don’t we try to get something right first time for once?

DECC have launched yet another review of FITs. It seems like just yesterday I responded to their fast-track review. Don’t try and read this in DECC’s amazing non-scrolling spreadsheet (downloadable from their FIT fast-track consultation page) but I see I ended my answer to their question 2 (which mostly consisted of expressions of astonishment that they had no effective mechanism for controlling the cost of FITs) by saying:

“If the intention is to exclude investors altogether and encourage only those pursuing a low-carbon lifestyle or self-sufficiency, then the domestic PV tariff should be reduced by at least 50% immediately.”

which is only what they’ve gone and done!

Subsequent to sending off my response to the fast-track consultation back in May, I realised that the most efficient way of setting FIT rates would be by auction (it seems some people made this point in their responses back then). The latest consultation is another opportunity for me to make this point.

But there are even bigger (fitter?) fish to fry. Just in time (normally abbreviated to JIT, so maybe I can say “JIT for FIT policy…”!), the Royal Society held a two-day discussion meeting on solar power in mid-November. As you’d expect there was a lot of discussion of new whizzy technologies. But a couple of more prosaic points struck me:

1. Solar power generation in the UK is limited by the available space, David MacKay emphasising this point in particular.
2. New solar PV technologies – that might convert a greater proportion of sunlight into electricity – are finding it difficult to get to market. As costs are lowered for these technologies, “traditional” silicon-wafer based PV continues to build scale economies.

In other words, FIT policies and other government subsidies around the world are driving prices down for the wrong technology for Britain. We don’t want 10% efficient panels, we want to turn 30-40% of the energy in sunlight into electricity.

Now, if you have a roof of a limited size, then, once there are no subsidies and the cost of solar PV is competitive with other forms of energy, you’ll choose the most efficient technology that continues to yield cost savings compared to buying electricity. That is, you’ll consider panels of 10% efficiency, 15%, 20% and so on until the cost per additional kWh over the lifetime of the panel exceeds the value of the electricity generated.

But subsidies screw things up.

As usual.

Specifically, in the UK FIT scheme, you’re limited by the banding to a certain size of installation. For example, the tariff for an installation of up to 4kW capacity is 21p/kWh. For 4-10kW it’s only 16.8p/kWh. So installations are typically of just under 4kW capacity. If your roof can accomodate a cheap 4kW panel there’s no incentive to instal a more efficient panel. Or even to use the whole roof. The UK’s solar resource is being squandered.

There are many ways to address the problem. You could devise all kinds of rules and regulations to ensure people used more efficient panels to drive down the costs of the best technologies.

One simple approach, though, might be to base the banding on installation area, not capacity. That is, the highest tariffs would be for installations that used just a few square metres. This would provide an incentive to squeeze as much energy out of the space as possible. It would also be more equitable as it would favour the owners of large roofs much less than does the present system. Most important, though, such a scheme would provide a market to help bring down the cost of the technologies we need for the future.

The present system ensures that all the available FIT income will go to owners of large roofs. Because more efficient panels cost more per Watt, the Government will keep lowering the tariff in response to a surge of installations of less efficient panels as their price comes down because of scale economies.  The FIT will never be high enough to justify installations of more expensive, more efficient panels on smaller roofs.

Tariffs for installations starting at (say) just 5m^2 roof space (compared to around 25m^2 for typical panels in a 4kW installation today) would ensure there is a market for the more efficient panels.

The approach of FIT banding by installation area rather than capacity could be simply combined with auctions – that is, prospective PV generators would bid the lowest FIT they were prepared to accept for one of a quota of solar PV installations of a given area – up to 5m^2, up to 10m^2 and so on.

Here, I want to provide an up to date version of my “Explanation of Apparent Superluminal Velocity in the CERN-OPERA Experiment” (pdf) together with a few words of explanation. This version is significantly different from the one I included in a previous Uncharted Territory post. Postscript: This version has now been submitted to viXra.org, an alternative to arXiv that I came across yesterday.

To recap, my argument is that the neutrinos are travelling at the speed of light, but the speed of light varies slightly depending on direction, because of the motion of the Earth, which is travelling at an estimated 300km/s as measured against the cosmic microwave background (CMB) radiation, which, being the same in all directions, can be taken as providing a stationary reference. It is very difficult to measure the one-way speed of light directly, and the experiments that have been carried out have determined instead c, the “round-trip” light speed. The CERN-OPERA neutrino velocity measurement experiment has unintentionally measured the one-way light speed by comparing neutrino flight times with the expected flight time at c, determined by measuring the distance between CERN and OPERA and successfully transmitting the time at CERN to the OPERA neutrino detector.

The reason for the new version is that I was a bit slow on the uptake. It was only on 27th October, just as I was about to submit to ArXiv, that I belatedly realised that the GPS doesn’t somehow use the “one-way” light speed, but provides a timing based on the “round-trip” light speed. At first I’d thought the whole problem was caused by the procedure for calculating the delay in the optical fibre used to transmit the timing signal over the last 10km into the Gran Sasso mountain to the OPERA neutrino detector. Then, around 25th October, I’d realised that sending a timing signal down an optical fibre runs into the same problems as moving a clock to measure a signal transmission time. On 27th I realised that the GPS also does something similar. A timing signal is sent from the GPS satellite to CERN and to Gran Sasso.

Schematic of CERN-OPERA neutrino velocity measurement experiment

In each case (using the labelling A – CERN, B – Gran Sasso and C – the OPERA neutrino detector) – (i) transmitting a timing signal via GPS from A to B, (ii) moving a clock from B to C to measure a delay in signal transmission, and (iii) transmitting a timing signal via optical fibre cable from B to C – you simply can’t use the time which the transmission has noted it was sent at to measure the speed of light. It’s slippery, but if you really concentrate on the problem, you’ll realise, as did Henri Poincaré, the hero of my previous post, that in each case you have to assume the light speed transmission time.

The best analogy I can come up with is if I received a letter from my nephew – undated, sent 2nd class, with an illegible postmark, as is usual these days – saying I’d forgotten his birthday. I’d be unable to pin down exactly when his birthday was. I’d have to guess how long the letter had taken to reach me.

Similarly, in case (i) in the CERN-OPERA experiment, a “common-view” timing signal is transmitted from a GPS satellite to clocks at CERN (point A) and Gran Sasso (point B), for the express purpose of synchronising those clocks. This signal simply includes the message “the time here is t_SAT”, where t_SAT is whatever the time is on the satellite’s clock. Now, the crucial point (which I only appreciated on 27th October) is that if the message takes n seconds to reach one of the clocks then it’s also n seconds out of date. Unless you know n you can’t tell what the time actually is at the satellite when you receive the message. This is established in the experiment by subtracting the distance from the satellite to the clock and dividing by c, the “round-trip” speed of light, adding the result to the time at which the message was sent. In fact, our whole system of Coordinated Universal Time (UTC) depends on subtracting the assumed transmission time of signals, determined by dividing distance by c, the round-trip light speed. Procedure (i) thus synchronises time between A and B, assuming light travels at c in both directions.

In case (ii) a clock is transported from a master clock at Gran Sasso (point B in the paper, synchronised with CERN by GPS) into the mountain to the OPERA neutrino detector (at point C in the paper) in order to establish the transmission delays in an 8.3km optical fibre (actually this is only the longest fibre in the experiment, but the argument is the same for the others). The transmission time, t_tr in the paper, is the time light would have taken to travel the distance of the cable into the mountain, plus the delays caused by the cable and associated equipment, which I’ve called t_sig. It’s t_sig we want to find out. But again, the signal includes no information about the duration of transmission at light speed. Again, if it takes n seconds to arrive, it’s n seconds out of date when it reaches the clock at the neutrino detector.

Case (ii), though, is slightly different from (i) and highlights the subtleties inherent in the problem. Here, we have a clock at C which we believe shows the time at B, assuming events at B and C are simultaneous. We can therefore establish the delay, t_sig, in transmitting the signal from B to C. But, if events at B and C are not simultaneous, as Einstein suggested, because of the Earth’s motion, then the delay in (or early) arrival of the signal at C compared to light speed transmission from B is exactly matched by the delay in (or early) time at C compared to that at B. Once the clock is moved from B to C it is no longer synchronous with the clock left at B. This is analogous to the Sagnac Effect, whereby clocks have to be adjusted to allow for the rotation of the Earth, and clocks that are moved lose synchronicity. It is in itself an important result, and I intend to devote a post solely to this point (though I don’t always keep my promises). Returning to the CERN-OPERA neutrino velocity measurement experiment, the outcome is that we’re no better off physically moving a clock from B to C than we are transmitting the time from B to C. We always obtain the same delay, t_sig. It might be worth noting that, in the experiment, the same t_sig was obtained by a different procedure (the two-way fibre delay calibration procedure) that doesn’t depend on physically moving clocks.

In case (iii) we do actually transmit a timing signal from B to C along the fibre-optic cables, using the calculation of the delay obtained in procedure (ii). We don’t know how long the timing signal takes, because, again, if it takes n seconds to transmit, it is n seconds out of date, but we assume the delay compared to light speed transmission is t_sig. Thus, the expected time of flight over the entire neutrino flight path has been calibrated based on c, the round-trip light speed – the time of arrival of the timing signal at C against which neutrino flight times are compared is t_A + x_3/c + t_sig (where t_A is the time at A, CERN, when the neutrinos were created and x_3 is, as in the paper, the distance from A to C).

It has to be said that the CERN-OPERA team have done a good job. I’m convinced they are excellent experimenters. The problem is theoretical. It appears they succeeded in establishing a timing signal at point C, the OPERA neutrino detector, that very accurately represented the arrival time of neutrinos emitted from point A, CERN, based on a round-trip light-speed, c, neutrino velocity. The trouble is the neutrinos were only travelling one-way.

The method I’ve adopted in the paper to demonstrate the point is to show that the measurements to determine the expected neutrino flight time at light speed, that is those used in the calculation of the timing signal delay at C relative to A, would all be the same for an observer moving relative to the experiment, but the actual neutrino flight time would depend on the motion of that observer. This is the point of the Lorentz transformations in the paper.

The experimenters have assumed they are stationary relative to the neutrinos, but since the neutrinos arrived earlier than expected, this is clearly not the case. The paper therefore goes on to calculate the velocity of the experimenters relative to the neutrinos, or to be more precise the “frame of reference” of the neutrinos. Because of the details of the experiment this can only be done in the average case. We can only determine one component of our motion relative to the neutrinos, that is that along the Earth’s axis. The rest of our motion varies with the Earth’s rotation and orbit and I assume these motions cancel out to zero.

This is where it gets really interesting. I can’t get the result to tally exactly with the Earth’s motion against the CMB. That leaves me wondering whether the problem is due to experimental error or real – in which case satellites such as WMAP have not measured our motion correctly against the CMB. If the problem is real, and we have measured something other than our motion against the CMB, then things could get very interesting indeed.

My argument boils down essentially to the point that I believe that light doesn’t travel at the same speed in every direction (relative to an observer on our moving planet, and according to our reckoning of time and distance) and the physics establishment does, for reasons that defy simple logic.

A couple of days ago I thought I’d see if I could find some books that shed some light (groan!) on the matter. What I was interested in was whether physicists are confused. I think it’s fair to say that they are.

I ended up tracking all the way back to Einstein’s seminal paper, On the Electrodynamics of Moving Bodies (1905). I found myself standing in Waterstones reading a translation in Hawking’s On the Shoulders of Giants, which basically consists of some reprints and a few pages of comment by the current Lucasian Professor. £22 (OK, £15 on Amazon) for a paperback. Nice work.

Anyway, it’s possible to find On the Electrodynamics kicking around on the internet (pdf), though not easily on the first page of Google’s results, which I guess tells you something straight away about the readership of the “most important scientific paper of the 20th century”.

Any reader of On the Electrodynamics can’t help being struck by the paper’s obvious shortcomings. Yes, shortcomings. Just because a paper includes brilliant, revolutionary ideas does not mean it is perfect in all respects. And On the Electrodynamics has two serious flaws which have perhaps contributed to today’s confusion:

1. References or, rather, the lack of them – Einstein’s assumption of isotropy
Einstein did not include any references in his paper. As a result, we simply do not know how carefully he’d studied certain works of the era. In particular, it makes it difficult to evaluate his opening arguments. My impression is that Einstein just wanted to focus on the crux of his argument.

Einstein first sets out his postulates, or assumptions:

“…the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the ‘Principle of Relativity’) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. [my stress]“

Maybe these postulates are only nearly true. The crux of my argument is that if the speed of light is independent of its source, then we always (except in one very special case) need to apply the same equations Einstein used (Lorentz transformations) to determine the speed of light relative to ourselves, the observer. We can’t just assume we’re the stationary observer! It’s a simple point.

Let’s read on a little more. Einstein is very particular about the need to reckon time in terms of synchronous clocks:

“If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ‘A time’ and a ‘B time’. We have not defined a common ‘time’ for A and B, for the latter cannot be defined at all unless we establish by definition that the ‘time’ required by light to travel from A to B equals the ‘time’ it requires to travel from B to A. Let a ray of light start at the ‘A time’ tA from A towards B, let it at the ‘B time’ tB be reflected at B in the direction of A, and arrive again at A at the ‘A time’ t′A. In accordance with definition the two clocks synchronize if:

tB − tA = t′A − tB

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:—
1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.
Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of ‘simultaneous’, or ‘synchronous’, and of ‘time’. The ‘time’ of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.
In agreement with experience we further assume the quantity

2AB/(t′A − tA) = c

to be a universal constant—the velocity of light in empty space.”

He’s going to go on, of course, to assume that the stationary clocks are in the “stationary” [sic] system, and show that the clocks will not appear synchronous to a moving observer.

But how do we know that light would travel at the same speed from A to B as from B to A? This need not affect the round-trip time.

One book I found in Ealing Central Library is devoted specifically to this issue of synchronising clocks. In Einstein’s Clocks, Poincaré’s Maps by Peter Galison, we find (p.217) that the French mathematician, well, polymath, really, Henri Poincaré, understood the problem of “true” and “local” time in 1904:

“‘[Lorentz's] most ingenious idea was that of local time. Let us imagine two observers who want to set their watches by optical signals; they exchange their signals, but as they know that the transformation is not instantaneous, they take care to cross them. When the station B receives the signal of station A, its clock must not mark the same time as station A at the moment of the emission of the signal, but rather that time augmented by a constant representing the duration of the signal.’ [wrote Poincaré - so far so good]

At first, Poincaré considered the two clock-minders at A and B to be at rest – their observing stations were fixed with respect to the ether. But then, as he had since 1900, Poincaré proceeded to ask what happened when the observers are in a frame of reference moving through the ether. In that case ‘the duration of the transmission will not be the same in the two directions, because station A, for example, moves towards any optical perturbation sent by B, while the station B retreats from a perturbation by A. Their watches set in this manner will not mark therefore true time, they will mark what one can call local time, in such a way that one of them will be offset with respect to the other. This is of little importance, because we don’t have any way to perceive it.‘ [my stress] True and local time differ. But nothing, Poincaré insisted, would allow A to realize that his clock will be set back relative to B’s, because B’s will be set back by precisely the same amount.’All the phenomena that will be produced at A for example, will be set back in time, but they will all be set back by the same amount, and the observer will not be able to perceive it because his watch will be set back’ [my stress]; thus, as the principle of relativity would have it, there is no means of knowing if he is at rest or in absolute movement. [my stress]“

Galison goes on (p.257ff) to speculate as to how familiar Einstein was in 1905 with Poincaré’s discussion of the idea of obtaining local time by the synchronisation of clocks. Regardless, when Einstein swept away the ideas of “local time” and “true time”, he took no account of the little difficulty highlighted by Poincaré. We can only speculate as to what Einstein thought and what he didn’t, but it would clearly have been more difficult to move away from the idea of the ether to that of relativity had it also been necessary to assume a “preferred” or isotropic reference frame relative to which the Earth is moving. That doesn’t mean it doesn’t exist, though. And, for my money, relativity includes a logical inconsistency. You simply can’t assume the light moves independent of its source and then perform transformations to show that the view of a moving observer of the reference frame in which the light is emitted perceives the light not to be moving at equal velocities in all directions relative to objects in the emitting frame, whilst those in the emitting frame magically do see equal velocities.

2. Unclear use of symbols
There’s one way to “rescue” Special Relativity. Let’s imagine you’re a confused young physics student. You might imagine that the Lorentz transformations retain equal light speed in all directions despite diagrams to the contrary, that is, you might pay particular attention to the qualification “length contraction not depicted” in representations of Einstein’s train thought-experiment.

You might define a thought-experiment (flashes when light from the centre reaches the ends of a moving train) and write something like:

“In fact [from the point of view of an observer on the platform] it [the moving train] is shorter in the same proportion as the second flash is later than the rear one.”

as Adam Hart-Davis does on p.231 of The Book of Time.

Hart-Davis appears to assume time-dilation and the relativity of simultaneity are the same thing. His calculations are then totally confusing (even if we ignore the fact that he presents calculations based on the length of the train before he’s told us how long it actually is and later says km/h when he means km/s!). The formula for calculating the time delay between flashes at the rear and front of the train as perceived by the observer on the platform is:

t = (1/√(1 – v^2/c^2))(τ – vx/c^2)

where:

• τ is the time difference as seen by the observer on the train
• t is the time difference as seen by the observer on the platform
• √ is supposed to be a square root sign – I’ve used ^2 for squared (can’t see how to get a superscipt on here)
• v is the velocity of the train (according to the observer on the train)
• c is the speed of light
• x is the length of the train (according to the observer on the train)

The term 1/√(1 – v^2/c^2) is known as γ (gamma) and can be ignored when v is small compared to c, as Hart-Davis does when calculating for a train moving at 22m/s.  The curious thing is, he also ignores γ when calculating the delay when the train is running at 200,000,000m/s and gets a 44ns delay.  He doesn’t explain this.

Hart-Davis then uses γ correctly to show the train looks only ~15m long (he implies this is exact – it isn’t) rather than 20m.

Presumably what Hart-Davis has done is assume that the length contraction of the train (a factor of ~0.75) cancels out with the time dilation factor (also ~0.75), the proportion by which time on the train runs slower than on the train. Is this correct? I guess so, though I’m not claiming to be 100% sure!

Nevertheless, the length contraction doesn’t cancel out the relativity of simultaneity – the signal still appears to take longer to travel to the front of the train from the perspective of the observer on the platform than from that of the observer on the train. The light simply has further to travel from the p.o.v. of the observer on the platform, as the front of the train is receding relative to the observer on the platform, but stationary relative to the observer on the train. The statement: “In fact [from the point of view of an observer on the platform] it [the moving train] is shorter in the same proportion as the second flash is later than the rear one”, is either totally confusing or simply incorrect.

You’d think they’d make a lot of effort to ensure accuracy in a book intended to inform, so maybe they’re confused.

And maybe it’s Albert’s fault.  If you take a look at On the Electrodynamics you might notice that Einstein uses “t” and “τ” (Greek letter small tau) to derive the difference (the formula above) between times observed by stationary and moving observers.  He then, breathlessly, one might imagine, rushes on to derive the time dilation factor (γ) in the rates of the clocks of the moving and stationary observers, using the same “t” and “τ”.  What he really meant to relate in the second case were, of course, “δt” and “δτ”.

Naughty Albert! It’s like Peter Crouch pulling the hair of the Trinidad defender to score in 2006.  He scored a goal, so we’ll ignore that little detail.

Or maybe Einstein was being deliberately obscure just to see if people really understood!

From Galileo’s Dialogues, 2020 edition, recently received by NeutrinoMail(TM).

This post supercedes my previous effort, since it includes an updated version of my paper on the CERN-OPERA neutrino velocity measurement experiment.  It complements my two earlier posts on the fast neutrino problem, the first being a general discussion of my explanation for the detection of apparent superluminal neutrinos and the second a detailed look at Einstein’s train thought-experiment.

They say a picture’s worth a thousand words.  I can tell you that’s a massive underestimate.  I could have bashed in 5,000 words in the time it took me to conceive of the following diagram, construct it in Powerpoint (is it really totally pants, or do I need a training course?) and most of all, tinker with it. And I’m still not sure it’s clear enough (comments welcome):

In Fig 1, I’ve shown a schematic of the neutrino velocity measurement experiment. It’s very simplified as the neutrinos were not sent exactly from the GPS at CERN. Similar errors may have occurred there as I am about to describe at the OPERA neutrino detector end of the experiment.

The aim of Fig 1 is to show that, over most of the neutrino flight path, all timing measurements were “one-way”:

• The neutrinos were transmitted from CERN to OPERA.
• GPS timing signals, used to synchronise the two GPS points shown, travel at light speed, which we perceive to be the same in all directions.
• Distances were measured either with reference to the GPS signals, or physically the old-fashioned way, in both cases within the Earth system of reference (ES) where we perceive distance to be equal in all directions.

But, crucially over part of the neutrino flight path, the experimenters have used the two-way light speed to determine the expected neutrino flight time. They had to do this because the OPERA neutrino detector is inside the Gran Sasso mountain to protect it from cosmic rays.

The question is whether the light “thinks” it moves at the same speed in all directions with respect to us here on Earth.

The answer is it doesn’t. Why would it? The Earth isn’t even a speck of dust over the distance light and neutrinos can travel. Light speed is nearly 30,000 times the Earth’s escape velocity. Neutrinos go through planets like bullets through tissue-paper. I could go on.

Fig. 2 attempts to show why light doesn’t “think” it moves at the same speed in all directions with respect to our experimental equipment.

First, Fig. 2a shows part of our planet as we perceive it. We perceive distances and therefore time the same in all directions. We set our clocks the same everywhere and assume that light simply takes d/c (the distance divided by a constant speed of light) to get from A to B, or CERN to OPERA in this case.

But, in fact, the Earth is moving, as shown by the fact that distant objects, such as what I recently saw a cosmologist term the rest frame represented by the cosmic microwave background (CMB) (this link has some good CMB schematics, too, btw), appear blue-shifted in the direction we’re moving in – the relative motion causes the photon waves to appear closer together – and red-shifted in the other direction. The CMB appears blue-shifted, not due south, but in a southerly direction (this is important).

Now, the fact that the planet is moving matters. Its speed relative to the CMB is about 600km/s or 1/500th light speed, which is significant when you’re trying to measure neutrino flight times to the nearest nanosecond (ns) or so.

I’m going to digress and explain why movement matters. Here’s another diagram (you really are being spoilt today!):

All we have to do is imagine we’re on a mission to Mars. Mission control are really sweating us – sending people to Mars is not cheap – but have said that we can have precisely one hour off each day to watch the 60 minute episodes of the second series of Firefly we’ve been waiting for for decades. After all, improved morale will increase efficiency.

Unfortunately, the PVR broke on landing so we can’t record the show or fast-forward through the ads. We have to be at the TV to catch the actual broadcast.

Now, if the show is broadcast at 8pm on Earth the time it will reach Mars depends on how far away we are at the time. Light takes 8 minutes to reach Earth from the sun, so I’m guessing that, during our mission, Mars could vary from being, say, 3 light minutes away from Earth to, say, 15, as illustrated in Fig 3.

Hopefully it is apparent that if we have a clock on Mars set to Earth time, we will have to adjust it continually as Mars moves further away from and closer to Earth as the two planets follow their different orbits around the Sun. The rate at which clocks appear to move on Earth as seen from Mars varies continually.

There is no absolute time, a common misconception.

Rather, relative time depends on distance and the relative rates at which time seems to pass depend on relative motion.

Returning to a consideration of Fig 2a, note that I have used no colour within the Earth part of the diagram. OPERA does not appear red-shifted to CERN even though OPERA is moving at 500km/s to the right in the diagram, because CERN is also moving at 500km/s to the right.

Now let’s consider how all this appears from the point of view of a neutrino (or light). Now, light can’t move at greater than the speed of other light. Such faster than light travel would effectively be the same as going back in time.

So light (and neutrinos) always travel at the speed of light, c, in empty space. If other objects are moving then they will perceive light to be red-shifted in the direction they’re moving from and blue-shifted in the direction they’re moving. The light waves are stretched (red-shifted) or squashed up (blue-shifted). As will be seen, it’s only by convention that we don’t instead consider the Earth as squashed up or stretched, which in fact might be a better fit to how the Universe actually is – as usual (sigh!) our perception is Earth-centric.

In Fig 2b, then, I’ve put the neutrino in the middle of its journey from CERN to OPERA (it might have been less confusing to have put it at the end, but the view forward is also interesting). Looking back, the neutrino would see CERN coming towards it at ~500km/s, due to the motion of the planet – the distance it has had to travel to OPERA is shortened (blue-shifted) by the Earth’s motion. This is true when the neutrino arrives at OPERA, so the neutrino has travelled less distance because of the motion of the Earth. It is not moving relative to the planet, but relative to all the other light in the Universe. It has to, otherwise some light would travel faster than other light, and that’s not what we observe.

Now to confuse the issue (probably a good job neutrinos can’t really see!). Looking forward, the neutrino sees OPERA moving away (red-shifted), but after it covers that distance, where it currently is (and CERN) will look blue-shifted. Got it? If it’s any help, this is exactly analogous to the discussion of Einstein’s train thought-experiment where, you will recollect, Bob was able to warn Alice, even though it seemed to Xavier that Agent Zero could reach her in less than d/c time in his near-light speed ship inside the train moving towards her, than the d/c he knew it would take Bob to warn her along the platform.

If the Earth is really moving, then, why don’t we reckon time to take account of that fact? Well, consider how awkward it would be (Fig 2b). Light would still travel at the same speed in all directions, but we’d dispense with the idea of time being the same in different places. Instead of having time constant everywhere and assuming that distances are the same in all directions, as we perceive, we’d have to assume time is different everywhere, and that it varies with distance depending on the motion of the Earth system. Or alternatively, we could keep an idea of time as the same over the whole planet and have distances vary depending on which direction we’re going in (as shown by the red-shift and blue-shift)!

Because we’ve forgotten these points that were long ago demonstrated in special relativity, and followed the convention to assume our time can be used to measure the speed of light and neutrinos travelling in all different directions – which it can’t – we’ve observed the neutrinos travelling as faster than they actually are.

The expected arrival time of the CERN neutrinos at OPERA should have been calculated taking into account the motion of the Earth, vE, as:

t=d/c – dvE/c^2

(or to be precise t=d/c – (dvE/c^2)/SQRT(1-v^2/c^2), but the denominator is insignificant at Earth’s velocity).

This can simply be understood (ignoring the complex version of the formula) as the distance the Earth would have moved in the time light travelled a given distance, divided by the speed of light.  It works out to about 5.6ns/km.  This is a maximum value, if the experiment were oriented directly in line with the Earth’s motion.

The precise distance that was measured without taking special relativity into account is uncertain, but the paper describing the experiment notes that there is a 8.3km optical fibre cable at San Grasso, though it’s the distance as the neutrino flies that is important.

The neutrinos appeared to arrive 60ns early.  Do the math.

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I’ve discussed this issue in much more detail in a paper Analysis of Flawed Fibre Time-Delay Calibration Methodology in CERN-OPERA Experiment v0.3 (pdf). I’d really like to post this on the open physics site, ArXiv, but I need to be endorsed by someone with the right credentials to do so. If anyone reading this can help, please contact me via this blog.

Here’s the Abstract for v0.3 of my paper (pdf):

The OPERA neutrino experiment at the Gran Sasso Laboratory, [1], obtained a measurement, v, of the neutrino muon velocity with respect to the speed of light, c, of (v-c)/c = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×10-5, that is, in excess of c by about 1 part in 40,000. Over most of the neutrino flight path from CERN to OPERA, distances and timings were established by GPS signals to within 2cm and (2.3 ± 0.9)ns respectively. These measurements are not problematic. The Gran Sasso Laboratory is underground, however, and a significant part of the measurement of the expected flight time at c was established using two separate fibre delay calibration procedures, both of which are based on the two-way speed of light rather than the reference-frame dependent one-way speed implicit in the GPS and the velocity of neutrinos over the (one-way) flight path from CERN to OPERA. The two-way light speed measurement ignores the moving frame of reference (the Earth system (ES)) in which the experiment was conducted and introduces errors of the same order as the early arrival time of the neutrinos (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns. Similar problems affect all attempts to measure the one-way speed of light [2]. This paper explains these problems, with reference to Einstein’s train thought-experiment and suggests how the expected one-way speed of light in a moving frame of reference such as the ES could be derived using the cosmic microwave background (CMB) as a stationary frame of reference. This problem is additional to the clock synchronisation issues described in [3], and can be traced to a flaw in a procedure, [5], which may have been used at CERN on other occasions, so may affect other experiments involving the accurate measurement of particle velocities approaching or at c. The experiment may yet prove to be important as it would, in fact, have measured a one-way neutrino (and hence one-way light) velocity and, by identifying a stationary frame of reference (possibly that defined by the CMB) with respect to light (and neutrino) transmission, perhaps shed light on cosmological questions.

The paper is a little more precise than the previous blog posts, but makes the same general point. I’d appreciate any comments. Here is the Abstract:

“The OPERA neutrino experiment at the Gran Sasso Laboratory obtained a measurement, v, of the neutrino muon velocity with respect to the speed of light, c, of (v-c)/c = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×10-5, that is, in excess of c by about 1 part in 40,000. Over most of the neutrino flight path from CERN to OPERA, distances and timings were established by GPS signals to within 2cm and (2.3 ± 0.9)ns respectively. These measurements are not problematic. The Gran Sasso Laboratory is underground, however, and a significant part of the measurement of the expected flight time at c was established using two separate fibre delay calibration procedures, both of which are based on the two-way speed of light rather than the reference-frame dependent one-way speed implicit in the GPS and the velocity of neutrinos over the (one-way) flight path from CERN to OPERA. This ignores the moving frame of reference (the Earth system (ES)) in which the experiment was conducted and introduces errors of the same order as the early arrival time of the neutrinos (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns. Similar problems affect all attempts to measure the one-way speed of light. This paper explains these problems, with reference to Einstein’s train thought-experiment and suggests how the expected one-way speed of light in a moving frame of reference such as the ES could be derived using the cosmic microwave background (CMB) as a stationary frame of reference. This problem is additional to the clock synchronisation issues described in Carlo Contaldi’s paper, and can be traced to a flaw in a procedure which may have been used at CERN on other occasions, so may affect other experiments involving the accurate measurement of particle velocities approaching or at c.”

This post attempts to prove that conclusion by a thought-experiment.

Let’s remind ourselves of Einstein’s train thought-experiment (figures from Wikipedia, copied here purely for convenience):

What Einstein demonstrates here is the relativity of simultaneity. Events (say light emitted at the centre of the carriage reaching the two ends) which are simultaneous in one frame of reference (top, from within the train) are not simultaneous in another frame of reference (bottom, from the platform).

I’d like to extend this slightly.

There’s even a little story. Xavier, in his hyperspeed train, has lured Bob to the train platform under the pretext of performing a relativistic experiment. He hopes to distract Bob for long enough to send Agent Zero to shoot Alice, who is also standing on the platform:

Consider a scenario where Xavier is at the centre of the train, and Bob is standing on the platform, each with their atomic clocks. Bob’s colleagues are also standing on the platform with their atomic clocks at the precise points where there are clocks on the train. Clearly, if set correctly, each pair of clocks would, for an instant, show the time in the other frame of reference – T1(train) would be the same as T1(platform) and so on.

Xavier doesn’t just want a pretext for his evil scheme. He also wants to perform an experiment. He wants to impress Bob by displaying Bob’s correct time on clocks at the ends of his train when he passes Bob on the platform. Bob’s clocks are synchronised by signals from T1(platform) so reflect light speed transmission delays in Bob’s frame of reference. Unfortunately for Xavier, he doesn’t know how fast his train will be moving relative to the platform at the moment he passes Bob.

How can Xavier get his clocks to show the same as Bobs’? There are two possibilities. He could either send a timing signal to each of the clocks at the ends of his train or he could walk the clocks from his position in the centre to each of the two ends. In the first case, the clocks would show the same as T1(train) adjusted for the transmission delays at the speed of light in the train. But we know from Einstein’s thought-experiment that these clocks will not show the same times as those on the platform. In the second case, the clocks would initially show the same as T1(train) but to show the same time as the corresponding clocks on the platform would have to be adjusted to reflect light transmission delays in Bob’s frame of reference. The adjustments would be different for the two clocks (the clock at the front of the train would have to be adjusted by more than the transmission time for light in the train and that at the rear by less).

It is evident from Einstein’s thought-experiment that neither method will yield the times on Bob’s clocks on the platform (Xavier would need to know the exact speed of his train relative to the platform and apply some equations from special relativity).

Signals sent at light speed to the clocks at the front and rear of the train will set them too early and late, respectively, since Bob sees events at the front of the train later than those at the rear. Similarly, walking the clocks from the centre of the train would ensure T1(train)=T2(train)=T3(train), but if adjustments are made to set T2(train) and T3(train) to be in synchrony like T2(platform) and T3(platform), T3(train) at the front would be behind T3(platform) and T2(train) at the rear would be ahead of T2(platform).

Xavier would either have to assume the speed of light was different in each direction or that time at the front of the train was delayed relative to time at the rear (and middle) of the train.

Let’s consider further what would happen if, on seeing Bob on the platform, Xavier told Agent Zero to set off in his near-light speed ship within the train (did I mention it was a big train?) in the direction of travel of the train, towards Alice, who Xavier knows is standing further along the platform in order to help Bob with the experiment.

Now, Bob is nobody’s fool, and sees Zero setting off (did I mention that the train is transparent?) and transmits a message to Alice: “Duck!”. She does so just before Zero arrives at T3(platform) (before he reaches the end of the train at T3(train)) and he misses. Obviously if Zero had reached Alice before the message from Bob, Zero would have travelled faster than light in Bob’s frame of reference. This is not possible, says Einstein.

Similarly, Bob might retaliate by sending Charlie in a similar near-light speed ship to shoot Yolanda at the rear of Bob’s train (which, again, he would reach before he came to the end of the platform). In this case, Xavier would be able to warn Yolanda.

The critical point is that both Bob and Xavier see light travelling at the same speed in both frames of reference. Apologies if you knew this already, but I enjoyed telling the story.

Not shown on my diagram is that Bob would have the same problem with clocks if he was also moving (did I mention the platform is a movable construct in space? – thought-experiment technology really has moved on since Einstein’s day!). If he passed Harry’s Bar on the Intergalactic Highway, he would have the same issues as Xavier (and if Harry also tried to shoot Alice in the same way – after all, he is simmering with jealousy after she ran off with Bob – Bob would also be able to warn Alice). Bob would have to assume either that clocks on his ship were delayed or that light travelled at a different speed along and against his direction of travel.

It follows that it is impossible to measure the one-way speed of light in any frame of reference since you either have to assume there is an error between all clocks in line of motion (proportional to distance) or that light travels at different speeds in different directions.

Unless, of course, you know that your frame of reference is stationary or exactly how you are moving in relation to a stationary frame of reference.

Now, Big Bang theory* tells us that the cosmic microwave background radiation (CMB) was all generated simultaneously. The CMB was generated throughout the Universe and what we see now is what’s reaching us from those regions in all directions that happened to be 13.7 billion light-years away at the time of the Big Bang. Clearly, therefore, the anisotropy (or redshift and blueshift) of the CMB is due to the motion of the Earth rather than that of the CMB itself.

The CMB therefore represents a stationary frame of reference.

As an aside, note that if neutrinos did travel faster than light, they’d eventually (in around 500 trillion years or so, based on the magnitude of the superluminal neutrino velocity reported for the CERN-OPERA experiment) reach a region of space where the Big Bang was still in progress, potentially interfering with their own creation. I don’t think the Universe would allow that, somehow. Alice would be miffed.

I therefore propose that if we adjust the fast neutrino timings to allow for the motion of the experiment, relative to the CMB, during the time the atomic clock was** moved between the GPS at San Grasso and the point where the neutrinos were detected, we will determine the true speed of neutrinos (which I predict will be that of light, c, within the limits of experimental error).

Note that the GPS timings and distances in the fast neutrino experiment do not contribute to the error, since all these are distorted in the same way (i.e. they are consistent within our frame of reference, or, to put it another way, systematic errors cancel out) due to the motion of the Earth (I may put up another post on just this point).

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* Just in case anyone assumes I’m an unreconstructed Big Bangian, I want to point out that I’m not entirely comfortable with Big Bang theory, but we can explain the difficulties of one-way lightspeed measurement and, by extension, fast neutrinos, within the paradigm. Obviously any replacement theory would have to explain all the Big Bang predictions (and more – but “more” doesn’t include fast neutrinos, since, just to be crystal, that phenomenon can already be explained) just as Einstein explained Newton’s.

** Postscript (15/10/11): It is incorrect to suggest that the time when the clock was moved (or clocks were synchronised) is important. My brain must have shorted at around the point I came up with that idea last weekend. In fact, the fibre time-delay calibration procedure (which uses two techniques based on the same misconception, one of which involves a transportable caesium clock) always gives the same result for the time-delay (excepting small measurement errors) based on an implicit two-way lightspeed measurement. The (one-way) neutrino flight time is on average greater than that expected based on the fibre time-delay calibration procedure (in this particular experiment, probably due to the N-S component of the CERN-OPERA neutrino flight-path), but dependent on the experiment’s orientation with the CMB when they are sent and detected (the change in orientation, as opposed to the motion, of the planet during their flight time is seriously insignificant). More detail on this point is included in the paper I have subsequently drafted on the erroneous superluminal neutrino result.  (Also made one unrelated wording change in the text, to clarify that the 500 trillion year estimate is based on the reported CERN-OPERA superluminal neutrino flight time).

Here’s my take on the whole business.

Note: After drafting this post I’ve come up with a systematic demonstration, by thought-experiment, of my assertion here that a correction needs to be made for the motion of the experiment relative to the stationary frame of reference represented by the cosmic microwave background (CMB) signal. When it’s complete I’ll jump in my neutrino-drive time-machine and add a link to it here.

Abstract

I’m convinced the neutrinos are not travelling faster than light, though the findings may tell us something useful. I believe the results have been misinterpreted or the experiment misconceived. It is not possible to validate the speed of neutrinos in the way attempted. I don’t believe the results are due to an experimental error as such. The problem is with the concept of synchronised time, necessary to establish a frame of reference for an experiment. The experimenters have synchronised time measurements over most of the distance over which they measured the speed of neutrinos by reference to the speed of light (via the GPS system). But over a significant distance they used a method involving the transport of timing devices. Such a method does not compensate for the motion of the local frame of reference and has introduced measurement errors leading to the apparent superluminal speed of neutrinos. Although we perceive the speed of light (and neutrinos) to be constant, time is distorted by the motion of the local frame of reference in relation to the rest of the universe (hence we see distant objects red-shifted or blue-shifted depending on their motion relative to us). The neutrinos have not agreed to be unaffected by the rest of the universe. The results could, however, be used to partially test the hypothesis that the frame of reference of the neutrinos (and, at least, light) is the whole universe, i.e. that they only appear to be travelling at equal velocity in all directions if this is measured against the cosmic microwave background (CMB) or average motion of the universe as a whole.

A Doubly Ambitious Experiment

The fast neutrino experiment measured the one-way speed of light (implicitly, by trying to establish the simultaneity of events) and then (explicitly) that of neutrinos, determining the latter to be in excess of the former. Now, the one-way speed of light has not previously been successfully measured. There are fundamental reasons for this which I will try to explain.

The fact that the literature which exists on the difficulty of one-way light-speed measurements is not discussed in Autiero et al suggests that this is the area in which the problem lies.

First, a little background.

What are Neutrinos Anyway?

I think it’s fair to say neutrinos are fundamental particles comparable in some ways to photons. If the fundamental property of photons is that they carry energy, maybe we can consider neutrinos to carry another form of energy (which we understand less and are less able to manipulate). Under certain circumstances the neutrino form of energy can be exchanged for the more familiar form of energy (so we can measure neutrino energy). I make this comparison and simplification to stress that our current level of knowledge suggests neutrinos should behave in some ways like photons. At least that should be the null hypothesis we should be aiming to falsify.

Why the Fast Neutrino Result must be false: (1) SN1987a

We already know neutrinos travel at the speed of light, to a very close approximation. Neutrinos from a distant supernova observed in 1987 (SN1987a) arrived 3 hours before light believed to have been emitted simultaneously, and there are reasons why the light might have been delayed. In any case, if the neutrinos had been travelling as fast as those in the fast neutrino experiment they would have arrived several years earlier. It’s therefore necessary to suppose there is something different about the fast neutrinos, such as their energy, even though there is no theoretical reason to suppose that this would be the case – the speed of light is not affected by its energy (which affects instead its wavelength). In fact the energy of the neutrinos in the fast neutrino experiment was several orders of magnitude greater than those from SN1987a. The obvious thing to do is to repeat the fast neutrino experiment with different energies. The critical question was asked about 1 hour 49 minutes into the CERN seminar (slide 83), by which time everyone was a bit tired. The answer was that no significant effect of energy on neutrino velocity had been determined. Referring to the fast neutrino paper (p.20), it’s clear that limited analysis, with significant uncertainty, has been carried out on only a small range of energies (varying by less than an order of magnitude and divided into just those of more than 20GeV and those of less than 20GeV).

Why the Fast Neutrino Result must be false: (2) Relativity

Relativity is not generally well-understood, but even Dara O’Briain on last week’s Mock the Week (a light-hearted UK current affairs TV show) noted that light doesn’t experience time. As far as light is concerned it travels instantaneously from point A to point B, assuming Einstein is right. Time passes only for stationary or at least slow-moving observers. In other words, time is associated with space, not with light itself. This is fundamental.

Simultaneity, Time and Frames of Reference

There’s some astonishingly good stuff on Wikipedia. I recommend the entries on Relativity of Simultaneity and Inertial frame of Reference. The point is we can only discuss events happening simultaneously within a closed system within which the relative velocities of objects are known. A frame of reference is not a property of the universe. Rather it’s something we need to define in order to apply physical laws. If we can assume we are taking measurements within a frame of reference, that is, that the phenomena (time, position, velocity, acceleration and so on) that we wish to relate are not independent of one another, then we can apply physical laws. For example, the fact that the solar system is hurtling round the Milky Way which is itself hurtling through space does not need to be taken account of in calculating a trajectory to land on the Moon.

And it’s only within a frame of reference that we can invoke a concept of simultaneity. Again, this is not a property of the universe, but something we need for our convenience. A concept of simultaneity allows us to relate time in different places.

Establishing a Frame of Reference: Conventions

Time always involves conventions, even when relativity doesn’t come into it. But when we want to make very accurate measurements we need further conventions. The main issue is how to deal with delays caused by the apparent speed of light. Consider a mission to the Moon. The communication delay is only a couple of seconds, but how does the astronaut know precisely when to expect a communication from Earth? There are a couple of sensible possibilities. The clock on the Moon could be arranged to show the time a message would arrive from Earth. The astronaut would not miss even a second of his favourite TV programme. A broadcast sent at 12 midday from Earth would arrive at 12 midday on the Moon. But when the reverse communication was attempted there would be a delay. Messages sent at 12:00:00 Moon time would reach Earth at over 2 seconds (the round-trip time delay) past 12 on Earth.

Less confusing is to pretend the time is the same on the Moon as on Earth. Messages sent at 12:00:00 from the Moon to the Earth will arrive at 12:00 and a bit over a second Earth time, and messages sent at precisely midday from the Earth will arrive at a bit over a second after midday Moon time.

Once relativity comes into it conventions have to be used to manage time even within a frame of reference. Or rather, a better way of thinking about it may be that conventions to manage time are required to establish a frame of reference. Remember, the universe doesn’t know anything about our frames of reference. They are just a means for us to apply physical laws somewhat more easily. We should always ask whether all the phenomena we are measuring are in fact entirely relative to our frame of reference. Otherwise we are not measuring what we think we’re measuring. It’s a failure to question the validity of the frame of reference that lies behind the apparent anomaly of “fast neutrinos”.

The fast neutrino experiment relied on a convention whereby all clocks indicate the same time as on a master clock (i.e. they simply tried to determine Coordinated Universal Time (UTC) with great accuracy at both the sending (CERN) and receiving points (the OPERA detector at Gran Sasso Laboratory in a mountain 730km away)). So the convention for communication is that all transmissions received appear delayed by a time dependent on the distance from sender to receiver (i.e. distance divided by the speed of light, c). At least, that is the aim, but as I hope to explain, this was not achieved. It is the limitations of this approach (rather than any errors in execution) that I believe causes the fast neutrino anomaly.

Establishing a Frame of Reference: Issues with Synchronising Clocks

There are a number of aspects of relativity that need to be considered when synchronising atomic clocks. These are well known from the experience of the GPS system (PDF), which relies on all satellites being synchronised to UTC. The fast neutrino experiment could not just rely on GPS, though, because the OPERA facility is underground. They also used “a two-way fibre procedure” (I don’t know what this is and neither does the internet) and, most importantly, “a transportable Cs [caesium] clock… yielding the same result” for a substantial distance (“an 8.3km long optical fibre” along which a timing pulse is transferred every millisecond).

There’s plenty to go wrong and some of the issues are discussed in a short paper by Carlo Contaldi (although written when it was not yet clear that GPS time synchronisation was used for the bulk of the transmission path, the points Contaldi makes are applicable to the residual time synchronisation). I agree with Contaldi that the fast neutrino experiment paper should have discussed this issue in much more depth, but am willing to assume that relativistic effects have been correctly accounted for, since two Metrology Institutes (Swiss and German) were involved. Whilst the level of accuracy may have been unusual, no new principles were involved.

One particular relativistic effect may be surprising. It turns out that simply moving atomic clocks, however slowly, introduces an error as a result of the Sagnac Effect. If you synchronise two clocks next to each other and move one from west to east (e.g. from CERN to OPERA) it gains time, i.e. a signal from CERN would take a little longer to reach OPERA. This is adjusted for in the fast neutrino experiment (and in GPS) by adding a correction to signal arrival times (you can’t just adjust the clocks because if you kept doing that right round the planet you’d end up with a clock around 200ns ahead or behind the one you started with). At the fast neutrino experiment seminar one person asked if they had “corrected for the Earth’s rotation”. One way of looking at the problem is that the light (or neutrino) is slowed down or speeded up by the Earth’s rotation against or in the direction of travel. But the light always appears to arrive at the same speed. So, even though the problem is resolved by adding a correction factor to each signal received, we have to think of the Sagnac Effect as a time distortion arising from trying to create a rotating frame of reference.

Extending Sagnac: What’s Been Overlooked

The Sagnac Effect is clearly a special case of a general effect. It’s not the result specifically of the Earth rotating, but of the Earth moving and taking with it the frame of reference we are trying to construct. If you were trying to measure the velocity of neutrinos instead in a space laboratory (with synchronised atomic clocks at each end, say), then you’d have to make a similar adjustment for the velocity of the laboratory.

Hang about! The velocity of the laboratory in relation to what? The experiment is being conducted in a closed space.

Well, to cut to the chase, my money is on the frame of reference for light and neutrinos being the whole universe. It’s unlikely to be something as small as the Earth or the Solar System, since most of the billions (trillions?) of neutrinos created at CERN will travel for light-years – only a hand-full were detected at OPERA (I heard that if you could shine a beam of neutrinos at a light-year thickness of lead, most of them would pass through).

Now, although the fast neutrino experimenters may have corrected for the Sagnac Effect (which GPS also corrects for) when moving their Cs clock, it may be the case that they didn’t correct for the Sagnac Effect motion of the Earth around the Sun, the Sun around the Milky Way or the Milky Way about the local supercluster. These are not corrected for in the GPS system, because these motions affect all the clocks (and light transmission between them) simultaneously (though I can’t help pointing out that small errors would arise if they failed to correct for the rotation of the Earth-Moon system about it’s the centre of gravity over a lunar month, but maybe they do!).

Most importantly, the red-shift/blue-shift dipole in the cosmic microwave background radiation (CMB) suggests the Earth is moving at about 6ookps (about 1/500th or 0.2% lightspeed).

Let’s come back to that.

Sources of Confusion 1: How could the motion of the Earth affect the neutrino speed measurement?

I’m confused so I expect you are too!

As with the Sagnac Effect, the motion of the Earth does not affect the speed of light or passage of time we perceive. It does, though affect time on Earth as perceived by an external observer (say one at rest in relation to the CMB). They would observe time running faster on Earth if it was coming towards them and going slower if it was receding. The time between pulses of light from Earth would vary and they would be blueshifted or redshifted.

Most importantly (as in Einstein’s train analogy), events that appear simultaneous on Earth do not appear simultaneous to the external observer.

The neutrinos (and light) are like the external observer. We might think clocks are simultaneous, but the neutrinos do not.

Sources of Confusion 2: Why don’t we notice this effect, say in the GPS system?

As in the case of the Sagnac Effect, the problem only occurs when you try to synchronise clocks. Once clocks are synchronised, then they all run slower or faster, as does every other physical process, as perceived by an external observer, as they change velocity relative to the external observer, e.g. as the Earth rotates and orbits.

Individual clocks may appear (to the observer) to speed up or slow down as they change orientation, as in the Fizeau experiment. Fizeau measured the difference in speed between light beams travelling through water flowing in opposite directions. If you were in one of Fizeau’s flows (but couldn’t detect the water flow – this is a thought experiment, OK?), it would be impossible to set two clocks to measure the speed of light without knowing the speed of the water flow.

Similarly, the errors in an experiment to measure the speed of light or neutrinos on Earth will depend on the orientation of the experiment with respect to the planet’s motion (such as its speed of 500kps relative to the CMB) at the time the clocks are synchronised.* (This has got a little chicken and egg, as we want to measure the speed of light and neutrinos to determine whether their frame of reference is the CMB. Try not to forget that the speed of light is not some external quantity, but actually determines time within a frame of reference, so appears constant, i.e. using time differences to measure the speed of light is circular. What the fast neutrino experiment was trying to do, of course, was measure the speed of neutrinos, by trying to calculate what the speed of light would have been had it been able to travel through the Earth with the neutrinos).

The GPS system synchronises time by the exchange of signals. These travel at the speed of light, which is common for the whole frame of reference. GPS doesn’t need to know about the motion of the planet as a whole (except for its rotation), since all positions are calculated relative to each other within the Earth system.

In the Fizeau thought-experiment, if instead you used the speed of light to synchronise clocks within the water flow, you could then use them to determine positions just as in the GPS.

Sources of Confusion 3: the Aether versus Frames of Reference, Mitchelson-Morley versus Sagnac and Fizeau

I’ve noticed that a number of people have pointed out on blogs that errors might have arisen in the fast neutrino experiment because of the motion of the Earth. They’ve been slapped down by others saying there’s no “aether”, as supposedly shown by Mitchelson and Morley (M&M). The idea of the aether was that there was a substance through which all objects move, which some argued exerts a drag in a preferred direction. Mitchelson and Morley showed this was not the case by demonstrating that light travelled at the same (2 way) speed in perpendicular directions.

This helped Einstein develop a theory without the aether concept. But he nevertheless needed to explain findings like those of Sagnac and Fizeau which appeared to show the existence of an aether.

The Real Meaning of the Fast Neutrino Experiment

When I thought the fast neutrino experiment had involved transporting clocks over 730km, I calculated the error as too large – up to 730km/500 (assuming the Earth is travelling at roughly 600kps or 1/500th light speed relative to the CMB, as discussed earlier) or 1.46km distance or around 4900ns early, as against the actual 60ns. To have had only 60ns error (of course other timing errors may come to light) would have been to assume the OPERA clock was synchronised when the experiment was somehow moving only slowly in relation to the CMB (maybe perpendicular).*

But with only 8.3km to worry about (actually there are other segments where the same error might be made), the maximum possible error is around 8.3km/500 or 16.6m or around 55ns, around that which was observed. Trouble is, this assumes the experiment was oriented directly in line with the motion of the Earth in relation to the CMB. If records of exactly how and when clocks were moved* still exist and/or it is possible to repeat the experiment, it should be possible to determine orientations wrt the CMB, and hence expected timing errors, assuming there’s anything in all this.

Maybe the fast neutrino experiment has not proved that neutrinos travel faster than light, but rather suggests ways in which we might measure the direction and velocity of motion of the Earth with respect to the frame of reference of neutrinos (meaning the frame of reference in which they appear to travel at the same speed in all directions). Maybe this will turn out to be the whole universe (and therefore in agreement with CMB redshift/blueshift measurements), maybe not.

* Postscript (15/10/11): It is incorrect to suggest that the time when the clock was moved (or clocks were synchronised) is important. My brain must have shorted at around the point I came up with that idea last weekend. In fact, the fibre time-delay calibration procedure (which uses two techniques based on the same misconception, one of which involves a transportable caesium clock) always gives the same result for the time-delay (excepting small measurement errors) based on an implicit two-way lightspeed measurement. The (one-way) neutrino flight time is on average greater than that expected based on the fibre time-delay calibration procedure (in this particular experiment, probably due to the N-S component of the CERN-OPERA neutrino flight-path), but dependent on the experiment’s orientation with the CMB when they are sent and detected (the change in orientation, as opposed to the motion, of the planet during their flight time is seriously insignificant). More detail on this point is included in the paper I have subsequently drafted on the erroneous superluminal neutrino result.  (Also made one unrelated wording change in the text, to clarify that the Sagnac Effect is just one example of a general phenomenon).

Most annoyingly, of recent eruptions of which we obviously have the best data, Pinatubo (1991) is discussed in detail (p.54-69), but El Chichon (1982) is referenced only in passing and Agung (1963) hardly at all. In particular, there seem to be important differences between the climatic effects of the El Chichon and Pinatubo eruptions, which would have been worthy of discussion.

Nevertheless, Eruptions fills a gap between school-level and academic material and anyone interested in the subject will find it a stimulating read. Some other reviews are listed here, though how carefully Kate Ravilious read it for New Scientist is in some doubt as she seems to think Oppenheimer discusses “thick layers of ash in Greenland ice cores” rather than the varying sulphuric acid fallout in the cores.

I should say that whilst I read Eruptions to better understand the effects of volcanoes on the climate, the book does discuss the other nasty things volcanoes can do to you, and a great deal more besides.

Minor gripes aside, I presume Oppenheimer’s account reflects the current state of academic thinking about the effects of eruptions on climate. It is this about which I have concerns, that is, the science itself, rather than Oppenheimer’s account of it.

Let me outline what appear to be the central tenets of the current paradigm, and comment as I go along:

1. The climatic effects of eruptions are entirely due to sulphuric acid aerosols.
Volcanoes eject varying amounts of sulphur in the form of sulphur dioxide and hydrogen sulphide into the atmosphere at varying heights and in varying proportions to the total amount of ash, lava and other material. The sulphur reacts to form sulphuric acid aerosols which can remain in the stratosphere for months to years, where they reflect light (and absorb heat, which helps keep them aloft). There is therefore a “recipe for a climate-forcing eruption” (Eruptions, p.69ff).

Eventually the sulphuric acid aerosols descend, and a historic record of sulpuric acid loading can be derived from ice cores, principally from Greenland and Antarctica. Oppenheimer draws on work at Rutgers University by Chaochao Gao, Alan Robock and Caspar Amman (presumably et al – this must have ben a lot of work) to produce an ice-core volcanic index (IVI). He reproduces Gao et al’s graph (as Fig. 4.6, p.98), which I kept referring back to. Here’s my copy-paste from Rutger’s site (for some reason there are spurious double lines on my version – check back at Rutgers if confused):

The IVI replaces H.H. Lamb’s famous Dust Veil Index (DVI). The idea that particles of dust as opposed to sulphuric acid could reflect light away is rejected entirely, or at least the effect of dust is considered insignificant. I find this assumption dubious. For example, the eruption of Huanyaputina in 1600 apparently had catastrophic effects on the climate – causing the Great Russian Famine – yet was, according to the IVI, only about twice as severe as Pinatubo, which really didn’t have a huge effect. Its sulphur emissions are dwarfed by those of Tambora in 1815 and Kuwae in 1452, yet it seems to have had at least as much of a cooling effect. Unfortunately, instrumental temperature records don’t go back to 1600, so we have to rely on anecdotal evidence. Here’s what Brian Fagan says in The Little Ice Age (p.104):

“The volcano discharged at least 19.2 cubic kilometres of fine sediment into the upper atmosphere. The discharge darkened the sun and moon for months and fell to earth as far away as Greenland and the South Pole. Fortunately for climatologists, the fine volcanic glass-powder from Huanyaputina is highly distinctive and easily identified in ice cores.

Huanyaputina played havoc with global climate. The summer of 1601 was the coldest since 1400 throughout the northern hemisphere… Summer sunlight was so dim in Iceland that there were no shadows.”

It seems to me at least plausible that the effect of eruptions on climate is due to dust particles as well as sulphuric acid aerosols. Indeed, my main problem with the IVI (see the paper Gao et al, 2008, which is available to download as a PDF from the Rutgers site) is that not enough has been done to establish how closely ice core sulphate levels correlate with climate impacts of volcanoes. As well as the possibility that there are significant effects due to other kinds of particle, there are other potential complicating factors:

• varying proportions of stratospheric sulphuric acid aerosol may end up in the ice, so that the IVI only gives an indication of the severity of the climate impacts of the eruption;
• the amount of sulphate in the ice gives no indication of how long it remained as sulphuric acid aerosol in the atmosphere – obviously the amount of sunlight reflected away is a function of time as well as aerosol density;
• some of the sulphate in the ice may not have reached as high as the stratosphere to cause significant climate effects (this must surely distort the figures for Icelandic, such as Laki, 1783, and Alaskan eruptions).

We have a lot of data on recent eruptions, which would seem to provide a means of establishing the usefulness of the IVI, which might be a good idea before translating it into a dataset to be plugged into climate models, as Gao et al have done. I can see the appeal of such a mechanistic approach, but it seems to me that the effects of different eruptions vary more than a single variable (OK in most recent cases we also have a date, or at least a season) would seem to suggest.

One problem with the IVI is that although it includes Pinatubo (1991), it does not include El Chichon (1982) because not enough of the Arctic ice cores were old enough, and there is no signal for El Chichon in the Antarctic (I’m unclear why a full signal for Pinatubo is apparently included). This misses a golden opportunity to validate the data. Clearly we need to get out to Greenland and drill more ice cores before the whole lot melts.

A further problem is that the IVI does not explain all of the data. For example, the cold period in the 1690s, including the exceptionally cold summer in 1695, as well as the record cold summer of 1725 (see my recent post on the cold summer of 2011) are completely unexplained. Note that the 1690s has long been a problem. Lamb interrupts his DVI list to discuss it (note the criticism of subjectivity which may affect the whole DVI – the eruption data may be deduced from the weather data rather than independent of it). Here’s a screen grab of part of the DVI which is accessible on Google Books:

Excerpt from Lamb, Climate: Past, Present and Future

More recently, I’d understood* that the dip in temperatures at the start of the 20th century was due to the Santa Maria eruption of 1902 (not to be confused with the famous Mount Pelee eruption of the same year, which is notable for causing a large number of fatalities). But there is only a small signal in the Gao et al data for 1902 (3.77 compared to 30.09 for 1991, the year of Pinatubo, limiting Gao et al’s spurious accuracy perhaps less than I should!).

* e.g. in the IPCC figure produced in a previous post.

2. Eruptions may affect only one hemisphere.
Tropical eruptions can have effects on both hemispheres, depending on (apart from the characteristics of the eruption and the weather at the time) latitude and time of year (and hence the position of the inter-tropical convergence zone, ITCZ). In their paper, Gao et al in fact separate out the hemispheric sulphate records:

Pinatubo affected both hemispheres, but El Chichon only the northern hemisphere (NH). El Chichon, though, seems to have reflected away at least as much heat, having produced a volcanic cloud “extending from the Equator to 30 deg N for more than 6 months, and then gradually spreading more widely” (Alan Robock, 2002, PDF). We can see this first in the atmospheric transmission of solar radiation record from Hawaii:

and, more to the point, in the record of oceanic heat content, where the dip in the early 1980s seems to have been greater than that in the early 1990s (though perhaps already underway by the time of the eruption):

So, if El Chichon removed more heat from the oceans than Pinatubo, and removed the bulk of it from the NH, you might expect some kind of effect on the Arctic ice. Here’s the annual ice extent for August 1979-2011, from the (US) National Snow and Ice Data Centre (NSIDC):

1983 and 1991 both seem to be above the annoying blue trend line (I always feel you need a better reason for drawing lines through data than that you feel like it!), but one might expect the effect to take longer than one year to play out. Indeed, if you imagine replacing the annoying blue line with one from around the turn of the millennium when one might suppose the effects of the two eruptions to have played out, the trend would seem to be a lot steeper. Maybe this tells us nothing more than that the eruptions cause a bit of an ice melt backlog, but I just thought I’d throw that point in.

Perhaps resolving the puzzle a tad, Realclimate have helpfully drawn my attention to ice volume data from PIOMAS, which I copy here purely for convenience:

This perhaps shows more clearly the greater effect of El Chichon (1982) than Pinatubo (1991) on the Arctic ice, though, again, we have trend-lines that confuse the issue, and, again, the eruption occurred somewhat after the temporary ice volume minimum at the start of 1982, and could not have influenced ice volume until at least mid-1982. Notwithstanding, if, here, one ignores the blue line and confidence-interval shading, one might postulate that the combined effect of the two eruptions was to negate any ice-melt that would have otherwise occurred – due to global warming and the fact that if the ice builds after eruptions, logic suggests that it must melt in their absence – for almost two decades, from 1982 to the turn of the millennium, and tentatively conclude that we’re now playing catch-up.

3. Tropical eruptions are climatologically more important.
The theory (Eruptions, p.72-3) seems to be that high latitude eruptions have less effect on climate, though time of year is obviously critical. Although Laki (1783) had dramatic effects on the climate, at least for a year or two, it was a very large eruption.

Oppenheimer briefly mentions the case of Kasatochi (August 2008), a moderate sized sulphur-releasing eruption in Alaska, and the most significant climatologically since Pinatubo (1991). Sure enough, you can see the signal in the Mauna Loa, Hawaii record, above (now I realise I should have numbered the figures). And here’s the possibility of an effect in another ice extent representation from NSIDC:

Not very conclusive**, but maybe the ice did start to re-form a bit quicker than usual in 2008.

** See also the Postscript to this post.

4. The climatic effects of eruptions last only for a few years.
There seems to be an emphasis in the literature on the short-term effects of eruptions. Presumably this is because an event, such as the eruption of Pinatubo, attracts a burst of interest – and generates a flurry of publications – for a few years, before everyone moves on to other projects. Oppenheimer (p.76), suggests forcing lasts around 3 years, after which aerosols disperse, temperature is affected for around 7 years, and sea-ice “perhaps for a decade”. But, he says, oceanic circulation “can be perturbed for up to a century”. Surely this in turn would affect climate? The emphasis on transient effects seems to conflict with the reconstructions of historic temperature records, when, I understood, the main explanation for century-scale variability (the Little Ice Age and all that) is the pattern of natural forcings, principally volcanic eruptions. The story doesn’t appear to be entirely straight, and perhaps this is due to an emphasis on debunking the idea that supervolcanoes (such as Toba 73kya) could have plunged the Earth “back into the ice age” (Oppenheimer, p.190ff).

5. The climatic effect of eruptions scales less than linearly – larger eruptions do not have a proportionately greater effect.
The theory (Oppenheimer, p.191-2) seems to be that larger eruptions produce so much sulphur that larger sulphuric acid particles form, which descend through the atmosphere quicker, so that larger eruptions (as indicated by the sulphuric acid loading in ice cores) do not have proportionately greater effects on the climate.

This all seems a bit speculative. I would have thought a sufficient explanation was that, assuming larger eruptions don’t affect the atmosphere for longer than less extreme events (you’d expect similar sized particles to descend at a similar rate however many of them there are), it seems impossible for effects to scale, given the amount of sunlight reflected away by even relatively small eruptions like Pinatubo and El Chichon (see the Mauna Loa diagram, above, again!). After all, there’s only so much sunlight to reflect away, so (as for greenhouse gases) the energy gain (negative in the case of volcanic aerosols) will be a log function of concentration.

6. The effect of eruptions is to produce cool summers and mild winters.
Except when they don’t.

This is a very confusing aspect, perhaps complicated by the small sample size of recent eruptions. There’s also a need to clarify what is meant.

It’s certainly true that it’s rare for the year of an eruption to experience a cold NH winter. This is what I naively expected when I first started looking at the Central England Temperature (CET) record – eruptions cool the planet, so winter should be colder, right? But in fact cold winters do not immediately follow eruptions, with one notable exception – 1784 after Laki, which also produced a hot summer (Oppenheimer devotes his chapter 12, The haze famine, p.269ff to this event, a repetition of which would, even, or maybe especially, in the 21st century, present serious challenges to health, transport – especially air – and agricultural services in Europe and maybe the entire Northern Hemisphere).

The general story seems to be that eruptions produce more zonal weather at least in the short-term, by heating the stratosphere and disrupting poleward heat transport by the large-scale atmospheric circulation. This leads to mild winters in western Europe (i.e. the zonal pattern of westerly airstreams dominates).

It seems to me there must also be an immediate effect on patterns of oceanic temperature and heat content. I’ve noted before that it appears volcanoes can trigger or exacerbate El Nino events, although this seems to be an area of controversy. Among other effects this may tend to produce mild NH winters.

But perhaps there are also persistent effects on patterns of oceanic heat content, thought to determine NH winter weather in particular. For example, there were generally mild winters in the UK at least for more than a decade after Pinatubo. Yet cold winters – and often runs of colder than usual winters – followed a few years after Huanyaputina (1600 – 1607 was extremely cold); the unknown 1809 eruption (General Winter defeated Napoleon in 1812 and 1814 was the last Thames Frost Fair); Katmai (1912 – 1917 was particularly cold); an eruption in 1925 which has a similar ice-core sulphur signature to Katmai (1929 was cold); Agung (1963); and El Chichon (1982). It’s a confusing picture, and it’s possible that these eruptions simply occurred during series of cold winters (e.g. the famously cold winter of 1962-3 was over by the time of the Agung eruption). Nevertheless, a hypothesis might be framed to relate the location (and season) of eruptions and hence their differential effect on ocean heat content in different regions (or just latitudes) to their effect on climate over a decade or more, through intensifying or weakening (or, in the case of the largest eruptions, completely overriding) the underlying multi-decadal cycles, such as the Atlantic Multi-decadal Oscillation (AMO).

Scientists often give the impression that they’ve answered all the questions. It’s often seemed to me that this puts off those most inclined to produce radical new ideas from specialising in the disciplines that seem to be “solved”. That is certainly not the case with the effect of volcanic eruptions on climate. There are more questions than answers. And, if the historic record is not enough, new events to investigate occur every few years. I’ll certainly be keeping an eye out for new developments in the field.

Postscript (2/10/11): Amended post to tidy up section on cold winters following eruptions, adding a reference to the 1809 event (location unknown) and to scale down some of the diagrams so they’re less in your face. Also, the figure below (from JAXA via Realclimate), perhaps shows the more than usually rapid ice build in 2008 more clearly than the NSIDC figure above, though you have top look closely at the spaghetti to see that the 2008 dark green line shows one of the lowest September ice extents in the period covered turning into one of the highest extents by November:

The Economist agrees with most observers that the problem boils down to how to deal with Greece.

Let’s recap.  Greece, a serial defaulter, essentially fiddled the books to understate its debt in order to be admitted to the euro club, hoping for more economic stability.  Then the financial crisis came, and, as the saying goes, the tide went out and the Greeks were seen to be wearing no trunks.  Not only that, there was an Aegean tsunami on the horizon. Luckily, the Germans had grabbed the deck-chairs so the Greeks aren’t on their own.

What are the Greeks, the Germans and the eurocrats (not to mention the IMF) to do?

What baffles me is the current hysteria from all quarters. Decisive action is not required, as for example, George Osborne insists. The Greek debt is a long-term problem which requires a long-term solution. “Decisive action” implies some kind of quick fix. “Decisive action” is the last thing we need.

In fact, I can see things that can be done to mitigate the situation – economic stimulus measures in the less-indebted eurozone, other European (that includes the UK, Mr Osborne) and other global economies – but I simply can’t see how the central problem could be handled any better than it already is. If that’s not what the markets want to hear then the markets will just have to get over themselves. Some problems just have to be lived with.

Let’s consider the alternatives (I’ve previously written about this on Martin Wolf’s blog at the FT, but I can’t even access that right now, as I terminated my FT subscription in protest at them trying to jack up the price).

1. Greece exits the euro and devalues
This would be catastrophic, at least in the short-term. The Economist discusses the possibility and quotes an estimate that such a step would cost Greece 40-50% of its GDP in the first year (though this seems to assume they leave the EU as well). The trouble is, the “mother of all financial crises” that would result would not be confined to Greece. French and other eurozone banks would take a massive hit, with all kinds of knock-on effects. Even if the initial shock could be contained without seriously recessionary consequences for the remaining eurozone countries, it would simply be a case of “who’s next?” – Ireland, Portugal, Spain, Italy, Belgium, France…

2. Greece devalues within the euro
This is the straw that many are now clinging to, including the Economist, but in fact it’s almost as bad as option 1.

First, there’s the moral argument. Why should the beneficiaries of excessive Greek borrowing be forgiven their debts? Greek taxpayers (or non-payers, by all accounts) would escape paying taxes equivalent to the nation’s long-term spending; all Greeks would have benefited from public services that they haven’t fully paid for; Greek public sector workers would have been paid more than the nation could actually afford – the list is endless. The point is, although different Greek constituencies would no doubt blame each other, the entire nation is complicit, though pre-school children can legitimately claim not to have been in a position to influence matters overmuch.

Second, if Greece is let off a large chunk of its debt, why wouldn’t other countries demand the same? Why should the Portuguese, Spanish, Italians, Irish, French and Belgians suffer tax rises and cuts to their public services if Greek debt is simply written down?

Third, and critically, there’s the problem that a Greek default within the euro doesn’t actually solve the underlying problem. It does something about the debt, but not the deficit. If Greek debt is (say) halved from around 140% of GDP to around 70%, they will still not be credit-worthy, because they’d still be running a deficit. There would still be a need for the IMF, EU and ECB troika to help the Greek government somehow bring revenue and expenditure into line. There’d still be a need for wealthy Greeks to pay more taxes, the Greek public sector to spend less and its economy somehow to grow. In the meantime there’d still be a need for someone to lend euros to Greece.

A Greek default within the euro would simply not have the usual effect of sovereign defaults because it would not be accompanied by devaluation.

In fact, the main effect of Greek default within the euro would be for the Greeks to say “thank you very much”. There’d still be a big hit on eurozone banks (including the Greek ones which would need to be recapitalised from somewhere, and not to mention the ECB), although not the automatic loss from lending to the Greek private sector that would occur in the case of option 1 (when devaluation would make it more difficult, to say the least, for Greek companies to service euro-denominated debt).

Now, it seems to me the troika must recognise this. If I was them I’d demand the budget reforms before allowing any kind of Greek default. In particular, the possibility of Greece having to leave the euro needs to be still on the table. In fact, it wouldn’t surprise me if there hasn’t been a nod and a wink to the off-message officials and politicians (usually German) who regularly float this possibility.

It seems the next payment to Greece is being put off to the last possible moment, even though stumping up is much better for everyone than the alternatives. What puzzles me is that the markets don’t recognise that this brinkmanship is a necessary part of the strategy of forcing Greece to balance its budget in the long-term.

What the Greeks should really be worrying about is the possibility that they haven’t resolved their fiscal problems by the time the rest of the eurozone has recovered (and in particular the banking sector has rebuilt its capital) sufficiently to withstand a Greek default, euro exit and devaluation. Then the eurocrats might just decide to throw them to the wolves.

Still, I wouldn’t rule out a collective loss of nerve and a Greek default within the euro. We’d have to muddle through somehow. If there’s a double-dip, there’s a double-dip – maybe that’s now the least we can expect; if there are further sovereign defaults, the sun will still come up the next morning; if we do end up calling it the Second Great Depression or a Lost Decade, life will still go on. As I said, some problems just have to be lived with.